I recently upgraded my PC from my laptop to a custom built desktop. I had no trouble running the Emulator on my laptop (besides the onboard graphics hassle of bad gameplay), but now that I have a dedicated video card, I'm running into problems.

With that being said; The problem I'm having is, PCSX2 doesn't pop open a window asking me for the ROM file, it just automatically starts and goes to the "Browser, System Configuration" Window that normal PS2's go to when there is no CD in the tray.

Does anyone know my problem? or a possible fix? I would be very greatful.

Click on Config--->Configure in the main PCSX2 window when you first start up the program and make sure the CD/DVD plugin is set to something other than CDVDNull(or whatever the blank plugin is called)

Yeah, that's the only thing I could think of that would cause that problem other than the game your are trying to play somehow losing compatibility with a newer revision of the emulator, which is prone to happen occasionally.